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<h1>Kendrick mass plot</h1>

<h2>Description</h2>
<p>
<h4>If you use this module for your analysis or visualization, please cite:</h4>
<dd>Three‐dimensional Kendrick mass plots as a tool for graphical lipid identification</dd>
<dd>A. Korf, C. Vosse, R. Schmid, P. O. Helmer, V. Jeck, H. Hayen, Rapid Communications in Mass Spectrometry 32.12 (2018): 981-991.</dd>
</p>

<h4>Parameters</h4>
<dl>
	<dt>Peak list</dt>
    	<dd>Select the targeted peak list.</dd>
	<dt>Peaks</dt>
    	<dd>Add peaks from the peak list.</dd>
	<dt>Kendrick mass base for y-Axis</dt>
    	<dd>Enter a sum formula which will be used as Kendrick mass base for the y-Axis.</dd>
	<dt>X-axis value</dt>
			<dd>Select which parameters you want to display on the X-Axis (Kendrick mass (KM) or m/z).</dd>
	<dt>Kendrick mass base for x-Axis</dt>
			<dd>If you want to display a Kendrick mass defect on the x-axis, check the check box and enter a sum formula as Kendrick mass base.</dd>
	<dt>Z-axis value</dt>
			<dd>Select which parameters you want to display in the third dimension. If you select "none", a 2D Kendrick mass plot will be generated.</dd>
	<dt>Kendrick mass base for z-Axis</dt>
			<dd>If you want to display a Kendrick mass defect on the z-axis in form of a heatmap, check the check box and enter a sum formula as Kendrick mass base.</dd>
	<dt>Z-axis scale value</dt>
			<dd>Choose the bounds for the Z-axis. "Percentile" allows to exclude values of a selected percentile bellow and/or above from the paint scale. Values below will be displayed in black, values above will be displayed in magenta. "Custom" allows to set custom ranges.</dd>
	<dt>Range for z-axis scale</dt>
    	<dd>Enter lower bound left and higher bound right. If you have choosen percentile for Z-axis scale the values must be between 0 and 100. If you enter 0 and 100, all values will be included in the paint scale.</dd>
	<dt>Heatmap style</dt>
		   <dd>Select the style of your paint scale. You can choose between rainbow and different monochrome color coded paint scales.</dd>
</dl>

<h4>Background</h4>
<dt>In 1963 Kendrick published his idea of a mass scale, the so called Kendrick mass scale, which is based on defining the mass of CH2 as 14.0000 u.⁠ The Kendrick mass scale is calculated by multiplying the IUPAC mass scale with the factor 14.0000 u/14.01565 u = 0.9988834. This results in the same mass defect for homologous components, the so-called Kendrick mass defect (KMD). The KMD is defined as the ∆ of a nominal Kendrick mass and its associated Kendrick mass. Using the Kendrick mass scale has the purpose of data reduction. More infos: https://en.wikipedia.org/wiki/Kendrick_mass<dt>
<p>
<h4>Formula for Kendrick mass and Kendrick mass defect</h4>
<p>
<img src="kendrick_mass_formula.png">
</p>
<p>
<img src="KMD_formula.png">
</p>
<p>
<dt>KM: Kendrick mass</dt>
<dt>KMD: Kendrick mass defect</dt>
<dt>R: Exact mass of selected base unit</dt>
</p>
<h4>Functionality</h4>
<p>
This module allows to create 2 and 3 dimensional Kendrick mass plots. All possible feature characteristics can be plotted in a third dimension. The plot window has a toolbar on the right side.
The first button changes the size of the blocks, the second toggle the background color between black and white, the third toggles the visibility of a grid and the fourth adds annotations for identified features.
</p>
<p>
<img src="screenshotWindow.png">
</p>
<h4>Shifting</h4>
<p>
The toolbar on the right side includes methods to manipulate the Kendrick plot.
</p>
<p>
One possibility is to shift KMDs. This is useful for extremely high or low KMD values.
</p>
<p>
<img src="shifting.png">
</p>

<h4>Charge dependent Kendrick mass plots</h4>
<p>
Fouquet et al. have shown how to overcome splits in Kendrick mass plots, which are caused by multiply charged ions. Considering the charge for the calculation of the KM leads to clustering of features.
</p>
<p>
<img src="charge_formula.png">
</p>
<p>
<dt>Z: charge</dt>
<dt>R: Exact mass of selected base unit</dt>
</P>

<p>
<dt>Fouquet, Thierry NJ, et al. "On the Kendrick Mass Defect Plots of Multiply Charged Polymer Ions: Splits, Misalignments, and How to Correct Them." Journal of The American Society for Mass Spectrometry 29.8 (2018): 1611-1626.</dt>
</p>

<p>
<img src="charge_dep.png">
</p>

<h4>Resolution enhanced Kendrick mass defect plots</h4>
<p>
Fouquet and Sato have shown how a fractional base unit (Divisor) can enhance the resolution of Kendrick mass plots.
</p>
<p>
<img src="fractional_base_unit_formula.png">
</p>
<p>
<dt>X: fractional base unit (integer > 0)</dt>
<dt>R: Exact mass of selected base unit</dt>
</P>
<p>
<dt>Fouquet, Thierry, and Hiroaki Sato. "Extension of the Kendrick mass defect analysis of homopolymers to low resolution and high mass range mass spectra using fractional base units." Analytical chemistry 89.5 (2017): 2682-2686.</dt>
</p>

<p>
<img src="fractional_base_unit.png">
</p>

<h4>Combining charge and fractional base unit (Divisor)</h4>
<p>
If both charge and fractional base unit are changed, the following equation is used:
</p>
<p>
<img src="charge_fractional_base_unit_formula.png">
</p>
<p>
<dt>X: fractional base unit (integer > 0)</dt>
<dt>Z: charge</dt>
<dt>R: Exact mass of selected base unit</dt>
</P>
<p>
<dt>Fouquet, Thierry NJ, et al. "On the Kendrick Mass Defect Plots of Multiply Charged Polymer Ions: Splits, Misalignments, and How to Correct Them." Journal of The American Society for Mass Spectrometry 29.8 (2018): 1611-1626.</dt>
</p>
<p>
<img src="KMD_charge_fractional_base_unit.png">
</p>

<h4>Remainders of Kendrick masses (RKM)</h4>

<p>
Another option to increase the resolution of Kendrick mass plots is the by Fouquet et al. proposed concept of RKM (remainders of Kendrick masses). By clicking the KMD/RKM button in the toolbar on the right side, KMDs are transformed to RKMs.
</p>

<p>
<img src="remainder_formula.png">
</p>
<p>
<dt> with {} being the fractional part function defined as x=x-floor(x)</dt>
</p>
<p>
<dt>RKM: Remainder of Kendrick mass</dt>
<dt>R: Exact mass of selected base unit</dt>
</p>

<p>
<img src="KMD_RKM.png">
</p>

<h4>Combining charge and fractional base unit (Divisor) for Kendrick plots with RKM</h4>
<p>
If both charge and fractional base unit are changed, the following equation is used:
</p>
<p>
<img src="remainder_charge_fractional_base_unit_formula.png">
</p>
<p>
<dt> with {} being the fractional part function defined as x=x-floor(x)</dt>
</p>
<p>
<dt>RKM: Remainder of Kendrick mass</dt>
<dt>X: fractional base unit (integer > 0)</dt>
<dt>Z: charge</dt>
<dt>R: Exact mass of selected base unit</dt>
</p>

<p>
<dt>Fouquet, Thierry, Takaya Satoh, and Hiroaki Sato. "First gut instincts are always right: the resolution required for a mass defect analysis of polymer ions can be as low as oligomeric." Analytical chemistry 90.4 (2018): 2404-2408.</dt>
</p>

<p>
<img src="KMD_RKM_charge_fractional_base_unit.png">
</p>

<h4>Further features</h4>
<p>
A double click on a data point opens a frame with an overview of the selected feature.
</p>
<p>
<img src="feature_overview.png">
</p>
<p>
A rainbow or monochrome color coded paint scale can be used for the third dimension. Depending on the dataset, a black background of the plot may result in a better contrast.
</p>
<p>
<img src="compareScales.png">
</p>
<p>
The contrast can be further improved by removing extremely high or low values from the paint scale. This can be achived using the "Range for z-axis scale" parameter. Features above the limit are displayed in magenta, features below the limit are displayed in black.
</p>
<p>
<img src="compareContrast.png">
</p>
<p>
Furthermore, identified features can be labeled using the last button of the toolbar on the right.
</p>
<p>
<img src="compareLabel.png">
</p>

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